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Question 423330: how do i factor a trinomial such as: xsquared - 14xy -51ysquared
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! your trinomial is:
x^2 - 14xy - 51y^2
your factors will be in the form of:
(x-ay) * (x+by)
multiply these factors together and you will get:
x^2 + bxy - axy - aby^2
combine like terms to get:
x^2 + (b-a)xy - aby^2
since your original equation is:
x^2 - 14xy -51y^2, this mans that:
(b-a) must be equal to -14
ab must be equal to 51
it just so happens that if a = 17 and b = 3, then you will get:
x^2 + (3-17)xy - (3*17)y^2 which will become:
x^2 - 14xy - 51y^2
so, you need to make a = 17 and b = 3
the general form of your factors is:
(x-ay) * (x+by)
substitute 17 for a and 3 for b to get:
(x-17y) * (x+3y)
multiply these factors together to get:
x^2 + 3xy - 17xy - 51y^2
combine like terms to get:
x^2 - 14xy - 51y^2
your factors are:
(x-17y) * (x+3y)
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